A DA20 DEPARTING ON TEB 5 EXCEEDED THE INITIAL 1500 FT ALT BUT DESCENDED DOWN AFTER ATC REMINDER.

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ON DEP REVIEW OF TEB 5 SID WE DEPARTED TEB AND AT 400 FT TURNED TO 280 DEGS THROUGH 1500 FT. TURNED DIRECT TO HEADING. I CONTINUED CLB TO 2000 FT PREMATURELY. SID STATED WAIT UNTIL 4.5 DME THEN CLB TO 2000 FT. CTR SAID TO STAY AT 1500 FT SO WE STOPPED CLBING AND RETURNED TO 1500 FT UNTIL PROPER POSITION. ERROR OCCURRED BECAUSE WE STARTED RUSHING AS A CREW AND HAD SOME FAMILIARITY WITH TEB. WE MISSED THE 1500 FT HOLD DOWN ON OUR REVIEW PRIOR TO DEP WHICH IS AND ALWAYS HAS BEEN VERY THOROUGH. THE DEP ITSELF IS BUSY AND THERE IS A LOT HAPPENING IN SHORT ORDER. FOR FUTURE DEPS WE WILL SLOW DOWN AND MAKE SURE WE REVIEW THE SIDS AND STARS PRIOR TO ARPT TERMINAL AREA ENTRY. SUPPLEMENTAL INFO FROM ACN 688857: THE DEP ITSELF IS SOMEWHAT CONFUSING; ESPECIALLY BECAUSE IT REQUIRES TURNS; AND SMALL CLBS AT VERY LOW ALTITUDES. AS A CREW WE PRIDE OURSELVES ON A VERY RIGID SOP; CHKLIST USAGE; AND GOOD COMMUNICATION. IN THIS CASE WE MISSED ONE SMALL PART OF THE PROC IN SPITE OF THE FACT IT WAS CAREFULLY REVIEWED PRIOR TO DEP. THIS DEP IS CONVOLUTED AND OTHER PLTS HAVE COMPLAINED ABOUT IT.